把這式轉natural log

I am not sure if this is what the question asking. It would be better if you can show me the whole question.

p = (e^a - e^-b)/ (e^c - e^-d),
p*e^b/e^d=(e^a*e^b-1)/(e^c*e^d-1)
In(p*e^b/e^d)=In[(e^a*e^b-1)/(e^c*e^d-1)]
In(p)+In(e^b)-In(e^d)= In(e^a*e^b-1)-In(e^c*e^d-1)
In(p)+b-d = In(e^a*e^b-1)-In(e^c*e^d-1)
In(p)= In(e^a*e^b-1)-In(e^c*e^d-1)-b+d //